PV of Annuity Due
Present value of beginning-of-period payments with periodic discounting.
When to use: Use for monthly or quarterly lease/insurance payments due at the start.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PVA | Present Value of Annuity Due | Total present value of beginning-of-period payments | $ |
| PMT | Payment | Periodic payment amount (paid at start of period) | $ |
| k | Interest Rate | Nominal annual interest rate | % |
| n | Number of Years | Time period in years | years |
| m | Compounding Frequency | Compounding periods per year | integer |
Real-Life Examples
Example 1: Monthly Lease
A car lease costs $450/month due at the start of each month, 5% compounded monthly, 3 years.
Given
Step-by-Step
The total present value of the car lease is $15,068.06.
Example 2: Equipment Lease
$800/month equipment lease due at start, 8% monthly compounding, 4 years.
Given
Step-by-Step
The equipment lease has a present value of $32,988.10.
Frequently Asked Questions
Enter the monthly payment as PMT, annual rate as k, years as n, and 12 as m. This formula discounts each beginning-of-month payment back to today, giving you the total present cost of the lease.
The capitalized cost is the present value of all lease payments plus any upfront costs. This formula calculates the PV of the payment stream, which is the core component of the capitalized lease cost used in financial reporting.
The periodic version divides the annual rate by m and multiplies years by m to handle sub-annual payment frequencies. The (1 + k/m) multiplier adjusts for beginning-of-period timing within each sub-annual period.